SSS* is a best-firststate space search developed in 1977 by George C. Stockman for the linguistic analysis of waveforms [1] . In a later paper Stockman (1979) [2] showed how to use this algorithm to determine the minimax value of game trees. SSS* and it counterpart Dual* are non-directional algorithms for searching AND/OR graphs in a best-first manner similar to A*. They expand multiple paths of the search graph and retain global information about the search space, and search fewer nodes than Alpha-Beta in fixed-depth minimax tree search.

SSS*

In 1979 Stockman introduced SSS*, which looked like a radically different approach from Alpha-Beta for searching fixed-depth minimax trees. It builds a tree in a so-called best-first fashion by visiting the most promising nodes first. Alpha-Beta, in contrast, uses a depth-first, left-to-right traversal of the tree. Intuitively, it would seem that a best-first strategy should prevail over a rigidly ordered depth-first one. Stockman proved that SSS* dominated Alpha-Beta; it would never evaluate more leaf nodes than Alpha-Beta. Numerous simulations have shown that on average SSS* evaluates considerably fewer leaf nodes. Why, then, has the algorithm been shunned by practitioners?

SSS*, as formulated by Stockman, has several problems. First, it takes considerable effort to understand how the algorithm works, and still more to understand its relation to Alpha-Beta. Second, SSS* maintains a data structure known as the OPEN list, similar to that found in single-agent search algorithms like A*. The size of this list grows exponentially with the depth of the search tree. This has led many authors to conclude that SSS* is effectively disqualified from being useful for real applications like game-playing programs. Third, the OPEN list must be kept in sorted order. Insert and (in particular) delete/purge operations on the OPEN list can dominate the execution time of any program using SSS*. Despite the promise of expanding fewer nodes, the disadvantages of SSS* have proven a significant deterrent in practice.

The meager improvement in the pruning power of SSS* is more than offset by the increased storage space and bookkeeping (e.g. sorting OPEN) that it requires. One can safely speculate therefore that alphabeta will continue to monopolize the practice of computerized game playing.

Dual*

Dual* is the dual counterpart of SSS* by Tony Marslandet al[10] . The dual version of SSS* can be created by inverting SSS*’s operations: use an ascendingly sorted list instead of descending, swap max and min operations, and start at -oo instead of +oo.